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Isentropic processes in thermodynamics are fundamental to our understanding of numerous physical phenomena across different scientific and engineering fields. They provide a theoretical reference case for the evaluation of real thermodynamic processes and observations. Yet, as analytical relations for isentropic transformations in gas dynamics are limited to ideal gases, the inability to analytically describe isentropic processes for non-ideal gases is a fundamental shortcoming. This work presents generalised isentropic relations in thermodynamics based on the work by Kouremenos et al., where three isentropic exponents γ P v , γ T v and γ P T are introduced to replace the ideal gas isentropic exponent γ to incorporate the departure from the non-ideal gas behaviour. The general applicability of the generalised isentropic relations is presented by exploring its connections to existing isentropic models for ideal gases and incompressible liquids. Generalised formulations for the speed of sound, the Bernoulli equation, compressible isentropic flow transformations, and isentropic work are presented thereafter, connecting previously disjoint theories for gases and liquids. Lastly, the generalised expressions are demonstrated for practical engineering examples, and their accuracy is discussed. [ABSTRACT FROM AUTHOR]

In comparison, the specific energy demands of mechanical aerators range from 0.42 to 0.83 kWh/kg O SB 2 sb [13] and the specific energy demands of air jets range from 0.74 to 1.0 kWh/kg O SB 2 sb [12]. For practical applications the specific energy demand of such a cascade can be estimated as follows: The twisted regime of the hyperbolic funnel tested in this work has a specific energy demand of 0.01 kWh/kg O SB 2 sb (see Appendix A for calculation details). The authors showed SOTR values in a figure but did not mention how these values were calculated. [Extracted from the article]

Aeration is one of the most cost intensive steps in water and wastewater treatment due to the large energy requirement for the creation of large surfaces for sufficient gas exchange as well as for providing efficient liquid transport in order to exchange saturated liquid elements at the surface with unsaturated ones from the bulk. In this work we show that geometrically constrained vortices in a hyperbolic funnel are a promising aeration technique as they meet these criteria and allow oxygen transfer coefficients up to 50 h − 1 , a number significantly higher than that of comparable methods like air jets or impellers (<10 h − 1 ). [ABSTRACT FROM AUTHOR]

A horizontal electrohydrodynamic (EHD) liquid bridge (also known as a "floating water bridge") is a phenomenon that forms when high voltage DC (kV·cm−1) is applied to pure water in two separate beakers. The bridge, a free-floating connection between the beakers, acts as a cylindrical lens and refracts light. Using an interferometric set-up with a line pattern placed in the background of the bridge, the light passing through is split into a horizontally and a vertically polarized component which are both projected into the image space in front of the bridge with a small vertical offset (shear). Apart from a 100 Hz waviness due to a resonance effect between the power supply and vortical structures at the onset of the bridge, spikes with an increased refractive index moving through the bridge were observed. These spikes can be explained by an electrically induced liquid–liquid phase transition in which the vibrational modes of the water molecules couple coherently. [ABSTRACT FROM AUTHOR]